Personally ,I feel the idea of the cited subject may take a philosophical overtone.We have had our psyche fixated to visualize and see things in the order form of matter and space only.

To my mind , the order emerges in the lower dimension of any chaos.I mean to stress that for any chaos existing in any form ,the micro dimension of the same will have some order
inherent.The lowest level of investigation to the dimensions ,so far have gone to 10 raise to the power of minus 18 or so in angstrom units (The Big bang revisted in recent experiments of scientists)while the macro world has reached beyond the 10 raise to the power of 35 or so in imaginable & foreseable universe .

Now ,We know that the chaos takes place at any stage:Be it in macro cosmos or the micro world of photon and beyond.The only thing is that we visulise the chaos in our own vision though the same may be a forming a pattern of sort in a dimension just a step or two below.Go to 10 raise to negative side in micro dimensions.

From this analogy , I propose to bring the philosphical angle into the discussions.Any chaotic situation could be an indication of some better order emerging from a lower dimension of matter in and around us.Some people intend to gauge the same through crystal or some intuition or some brain wave and foretell us about the events to happen.However, what I perceive it needs to firm up like do we agree to the concept that chaos has some inherent order in it at some lower dimesnion.Does it indicate some change to happen to bring an order of higher dimension in to the Macro world.May be if this can be hypothesized and reserched in then looking at pattern in the lower dimesion can tell us some likelyhood of events at a larger world.

Kindly react for the thought process and the Micro & Nano scientists can help in investigating some patterns which can really forsee the possibilitiesof events in the world ,we live.

Only during the past few months have I finally seen that chaos and order can be better understood if they are not assumed to be in strict opposition, the kind of instinctive view that most of us had taken on board over the past quarter century.

Let me start out by emphasising that I am talking about chaos as understood in mathematics and science and not the looser popular understanding, that is where a chaotic system has some measures that are indistinguishable from random and where the smallest change in initial conditions can rapidly lead to a vast divergence in outcomes. Order is where you can make reliable long term predictions, chaos is where you cannot, but in other ways they are not so opposed.

In the universe of simple programs that is the subject of NKS, some programs exhibit either kind of behaviour depending only on the starting data. Wolfram defined this area of overlap as Class 4 in 1983 but since then there has been more focus on a hypothesised boundary between order and chaos, as well as by attempts to obliterate that boundary.

I was lucky enough a year ago to come across a previously obscure cellular automata rule which does a much better job than any other of making it clear that the actual source of complexity (the underlying question that inspires this whole field) is best seen as creative synergy between deterministic chaos and emergent order. In systems having a potential for complex behaviour, chaotic processes rapidly explore a vast range of configurations, some of which are found to be in attractor basins which lead to local cyclic states. And when those ordered states are sufficiently complicated they can accelerate the spread of chaos into previously empty territory.

A year into this project I'm mainly concerned with studying a growing diversity of developed forms that are produced from trivial seed patterns, but still discovering new local mechanisms which further expand the already vast range of possibilities. It is a central point of emergence that you cannot predict the macro from knowledge of the micro alone.

(My primary motivation for taking on such projects is the philosophical understandings they can bring into focus.)

Your questions are very relevant to where I am with this right now, Mike.

> But couldn't we also think of (order) as that moment where patterns in a CA converge?

I'm totally happy with thinking of patterns converging in the terms of attractor basins that others have long been working with. This was integral to my first ever post to NKS forum which on rereading emphasises how long I've been stumbling close to the idea of synergy between chaos and order. Only in the past couple of days I've starting thinking in the with the curse of hindsight blindingly obvious term of "tributaries" to describe convergent patterns, exemplified by the first part of a recent animation.

> Sure you can start out with some simple initial conditions, and come up with lots of patterns that diverge outwards from the beginning.

In the kind of strictly deterministic (model/"toy") systems that are easy to explore on computers there is no future divergence from exactly matched configurations, however systems which are statistically similar at one point of their iteration can diverge wildly later.

> But we notice patterns that also come to an end, do we not?

This is one of the things that has kept me interested in my current project. The most complicated localised orderly processes all have finite life spans. They typically require base structure formation which always occurs at 1 cell per 2 iterations (1/2 speed) enhanced by secondary processes which run at 2/3 or even 4/5 and thus eventually overtake and the 1/2 speed "engine" and terminate. Examples caught "in the wild" include:

In the wild, slightly simpler structures almost all have finite lifespans, some after relatively long and "interesting" (from an outside perspective) lives but many more after little lives. (There are also both finite and seemingly ever-growing emergent patterns that are immortal, but typically only four per viable seed pattern.)

> Maybe they'll start back up again, sure.

That implies a very deep question: Are they the same pattern, or a new pattern, or better still reincarnated? And how much divergence of detail does reincarnated stand?